A trolling plate is a device that is mounted to your motor, directly behind the prop. It creates a hydraulic pressure that slows the travel of the boat even though the prop is still turning faster than would otherwise be acceptable. By sock, I am assuming he is referring to a sea anchor. I too refer to is as a sock, as in wind sock. Same basic idea, just a little more heavy duty when we use them for water than the ones made for wind. A canvas cylinder with one large end tied to the boat and one small end trailing behind. The same can be done with the use of dragging buckets but they don't seem to work as well.
As to your question about trolling without a trolling motor, I must say that this depends on the boat that you have. If it is a 12 or 14ft boat with oars, you can troll by rowing around with them. If it is a 21ft deep-vee, I am assuming that you are trying to troll with a large motor and the advice given by SuperD I would consider to be sound advice. More information would be needed if you want to get a better answer.